ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

279 IRREVERSIBILITY-THE ENTROPY BARRIER
become steadily thinner as we have to introduce more and
more vertical subdivisions. This is expressed in Figure 41, sequence
B, where, going from top to bottom, we have ti = 1, 0,
- 1, and finally ti = - 2. We see indeed that the number of
boxes increa ses in this way from 4 to 32.
Once we have the boxes, we can compare the non-equilibrium
distribution with the equilibrium distribution for each
box. In the present case, the non-equilibrium distribution is
either a dilating fiber (sequence A) or a contracting fiber (sequence
C). The important point to notice is that when ti is
receding to the past, the dilating fiber occupies an increasing
large number of boxes: for ti = -2 it occupies 4 boxes, for
ti = - 2 it occupies 8 boxes, and so on.
As a result, when we apply the fo rmula given in Chapter
VIII, we obtain a finite result, even if the number of boxes
goes to infinity for tr-+ -oo.
In contrast, the contracting fiber remains always localized
in 4 boxes whatever ti. As a result, .Jl, when applied to a con-
A 8 c
Figure 41. Dilating (sequence A) and contracting (sequence C) fibers
cross various numbers of the boxes which subdivide a Baker transformation
phase space. All "squares" on a given sequence refer to the same time, t=2,
but the number of the boxes subdividing each square depends on the initial
time of the system ti.